On the structure of formal balls of the balanced quasi-metric domain of words

TL;DR

This paper investigates the structure of formal balls in a balanced quasi-metric domain of words, demonstrating that the associated poset forms a continuous domain, which advances understanding in denotational semantics.

Contribution

It proves that the poset of formal balls for the balanced quasi-metric on word domains is a continuous domain, providing new insights into the domain's structure.

Findings

The poset of formal balls is a continuous domain.

The structure extends previous work on quasi-metrics and semantics.

Supports the theoretical foundation for denotational semantics.

Abstract

In "Denotational semantics for programming languages, balanced quasi-metrics and fixed points" (International Journal of Computer Mathematics 85 (2008), 623-630), J. Rodr\'{i}guez-L\'{o}pez, S. Romaguera and O. Valero introduced and studied a balanced quasi-metric on any domain of (finite and infinite) words, denoted by $q_{b}$. In this paper we show that the poset of formal balls associated to $q_{b}$ has the structure of a continuous domain